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arXiv:2005.14432

The origin of correlation fringe in Franson-type experiments

Byoung Seung HAM

Published May 29, 2020• 3 citations
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Abstract

Nonlocal correlation is the key concept in quantum information processing, where quantum entanglement provides such a nonclassical property. Since the first proposal of noninterfering interferometer-based two-photon intensity correlation by Franson (Phys. Rev. Lett. 62, 2205 (1989)), the particle nature of photons has been intensively studied for nonlocal correlation using Mach-Zehnder interferometers (MZIs). Here, the role of MZIs is investigated with respect to the origin of nonlocal correlation in Franson-type experiments, where the wave nature of photons plays a critical role. Under the coincidence-provided quantum superposition between independent MZIs, we prove that nonlocal correlation can be created from non-entangled photons through the MZIs.

DOI
10.48550/arxiv.2005.14432

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Nonlocal correlation is the key concept in quantum information processing, where quantum entanglement provides such a nonclassical property. Since the first proposal of noninterfering interferometer-based two-photon intensity correlation by Franson (Phys. Rev. Lett. 62, 2205 (1989)), the particle nature of photons has been intensively studied for nonlocal correlation using Mach-Zehnder interferometers (MZIs). Here, the role of MZIs is investigated with respect to the origin of nonlocal correlation in Franson-type experiments, where the wave nature of photons plays a critical role. Under the coincidence-provided quantum superposition between independent MZIs, we prove that nonlocal correlation can be created from non-entangled photons through the MZIs.
Franson-type nonlocal correlation results in a second-order intensity fringe between two remotely separated parties via coincidence measurements, whereas the corresponding local measurements show a perfect incoherence feature. This nonlocal correlation fringe between paired photons is mysterious due to the local randomness in both parties. Here, the Franson nonlocal correlation fringe is analytically investigated using the wave nature of photons to understand the mysterious quantum feature. As a result, the nonlocal intensity fringe is turned out to be a measurement selection-based coherence feature, while the local randomness is from effective decoherence among broad bandwidth-distributed photon pairs. As a result, a coherence version of Franson nonlocal correlation is suggested for macroscopic quantum applications with a commercial laser. The local and nonlocal correlations of the proposed scheme show the same results as entangled photon-pair based Franson correlation. At the request of the authors, this article is being retracted effective 28 October 2022.
In a Franson interferometer two-photon interference fringes occur despite the photons never encountering each other [1]. This phenomenon is a fundamental demonstration of the nonlocal nature of quantum mechanics. It serves also as a direct proof of frequency-time-entanglement. Furthermore, it can benefit not only from local, but also nonlocal dispersion cancellation techniques [2], which is a very useful property when working with spectrally broad photon pairs. More specifically, one has to distinguish between dispersion occuring before the individual Mach-Zehnder interferometers (MZIs), which constitute the Franson interferometer, and within them. Analysis of influences up to second order has shown that no loss of contrast can be expected from dispersion before the Franson interferometer. Differential second-order dispersion inside the interferometer, however, can cause a reduction of contrast in the interferogram [3].
Indistinguishability in quantum mechanics is an essential concept to understanding mysterious quantum features such as self-interference of a single photon and two-photon nonlocal correlation. Delayed-choice experiments are for the cause-effect violation via post-measurements of photons in an interferometric system. Recently, a macroscopic version of the delayed-choice experiments has been demonstrated using the classical means of Poisson distributed photons in a noninterfering Mach-Zehnder interferometer (NMZI). Here, a coherence version of the nonlocal correlation is presented using the wave nature of photons in space-like separated orthogonally polarized NMZIs. For this, polarization-basis projections of the pair of NMZI output photons onto a set of polarizers are measured coincidently, where each output photon comprises orthogonal polarization bases. Because of the coherence feature of the output photons via coincidence detection, a phase sensitive nonlocal correlation is achieved. As a result, indistinguishability limited to a single or entangled photon pairs needs to be reconsidered with basis (polarization) randomness for the nonlocal correlation.
Franson-type nonlocal correlation is related to Bell inequality violation tests and has been applied for quantum key distributions based on time bin methods. Using unbalanced Mach-Zehnder interferometers, Franson correlation measurements result in an interference fringe, while local measurements do not. Here, randomness-based macroscopic Franson-type correlation is presented using polarization-based two-mode coherent photons, where the quantum correlation is tested by a Hong-Ou-Mandel scheme. Coherent photons are used to investigate the wave properties of this correlation. Without contradicting the wave-particle duality of quantum mechanics, the proposed method provides fundamental understanding of the quantum nature and opens the door to deterministic quantum information science.
Coincidence detection is a key technique used in nonlocal quantum-correlation measurements to test Bell inequality violation between remotely separated local detectors. With individual uniform intensity of local measurements, the nonlocal correlation fringe is a mysterious quantum feature that cannot be achieved classically. Here, the coincidence detection is coherently investigated to understand the fundamental physics of the nonlocal correlation fringe via second-order quantum superposition between selected nonlocal measurement events. Because of the coherence feature of paired photons, the coincidence technique modifies the measurement events for the rule of thumb of indistinguishability between selected measurement bases of paired photons. This indistinguishability is quantum superposition between nonlocally detected events resulting from a selected time slot of coincidence, where coherence between individually measured photons is an absolute condition.
Franson-type nonlocal quantum correlation based on the particle nature of quantum mechanics has been intensively studied for both fundamental physics and potential applications of quantum key distribution between remotely separated parties over the last several decades. Recently, a coherence theory of deterministic quantum features has been applied for Franson-type nonlocal correlation [arXiv:2102.06463] to understand its quantumness in a purely classical manner, where the resulting features are deterministic and macroscopic. Here, nearly sub-Poisson distributed coherent photon pairs obtained from an attenuated laser are used for the experimental demonstrations of the coherence Franson-type nonlocal correlation. As an essential requirement of quantum mechanics, quantum superposition is macroscopically provided using polarization basis-randomness via a half-wave plate, satisfying fairness compared with the original scheme based on phase bases. The observed coherence quantum feature of the modified Franson correlation successfully demonstrates the proposed wave nature of quantum mechanics, where the unveiled nonlocal correlation is relied on a definite phase relation between the paired coherent photons.